If there is something behind a horse, whatever it may be, their instinct is to move away from this pressure and to run away or kick out.
I suggest that when she jumps forward, make it your idea that you asked her to move forward and speed up. Put your leg on and make her work. Do lots of overtaking exercises in the school, allowing other horses to overtake yours while riding her. If she speeds up again, make her go faster and make her work. She will eventually realise that speeding up is actually much more hard work than relaxing and accepting the other horse. Continue to repeat this and praise her when she stays relaxed when a horse speeds up behind her.
Desensitising to things behind her is also useful, although I'd advise doing lots of groundwork to ensure your horse knows that you are her leader first, so the trust is already there. Begin by whipping the ground next to her. If she moves away, allow her to do so but do not stop whipping the ground. Allow her to find the correct answer, which is standing still and relaxed. As soon as she stops completely while you are whipping the ground, reward her by taking away the pressure and repeat. She'll soon learn that the scary noises around her will leave if she is relaxed and still, rather than running off. As you progress you should be able to desensitise to whipping behind her so she knows that if there is a sound behind her there is no need for her to run off.
Consistency is your best friend here, as well as patience. Make the wrong thing hard and the right thing easy.